Question

Find \( \cot^{-1} \left( \tan \frac{\pi}{7} \right) \).

• A. \( \frac{\pi}{7} \)
• B. \( \frac{5\pi}{14} \)
• C. \( \frac{9\pi}{14} \)
• D. \( \frac{3\pi}{14} \)

Hint:

To solve inverse trigonometric expressions, use the identity \( \cot^{-1} x = \frac{\pi}{2} - \tan^{-1} x \).

Answer 1

The Correct Option is B

We are given the expression \( \cot^{-1} \left( \tan \frac{\pi}{7} \right) \). Recall that: \[ \cot^{-1} x = \frac{\pi}{2} - \tan^{-1} x \] So, \[ \cot^{-1} \left( \tan \frac{\pi}{7} \right) = \frac{\pi}{2} - \frac{\pi}{7} \] \[ = \frac{7\pi}{14} - \frac{\pi}{7} = \frac{5\pi}{14} \] Thus, the correct answer is \( \frac{5\pi}{14} \).